Conditional expectation of a uniform distribution given a geometric distribution

Question

Let N follow a geometric distribution with probability p. After the success of the experiment we define X, a uniform distribution from 1 to N. Both distributions are discrete. Find E[X|N].

Answer 1

Guide:

Find $\mathbb E[X\mid N=n]$.

This is an expression in $n$ and if we set $f(n)=E[X\mid N=n]$ then $\mathbb E[X\mid N]=f(N)$.